2 Answers
2

Believe you me, people have devoted a lot of time to coming up with composite models of the electron, without much to show for it. For example, see:
http://en.wikipedia.org/wiki/Preon

High energy scattering experiments have shown that the charge radius of the electron is very small, and yet the rest mass of the electron is also very small. It's difficult (though not impossible) to achieve both in a composite model.

1) The standard model considers the leptons elementary particles. As it describes very successfully most of the data gathered by particle physics studies there is no reason to question the hypothesis of elementary leptons.

2)experiments testing for compositness of leptons give only lower limits for the scale of the appearance of compositeness. See for example this recent publication from LHC data for electrons and muons.